Question

Complete the following nuclear equation: \( \^{30}_{15}Si + ? \rightarrow ? + 1e^0 \)

• A. \( + 1e^0 \)
• B. \( 0 + 1e^0 \)
• C. \( 0 - 1e^0 \)
• D. None

Hint:

In beta decay, a neutron is converted into a proton, and an electron (beta particle) is emitted, maintaining the atomic number while the mass number remains the same.

Answer 1

The Correct Option is B

To complete the given nuclear equation, we follow these steps:

The initial equation is: \(\ ^{30}_{15}Si + ? \rightarrow ? + 1e^0 \)

In nuclear reactions, the sum of the atomic numbers (subscripts) on both sides of the equation must be equal, as must the mass numbers (superscripts).

1. Analyze the given equation:

• Initial isotope: \(\ ^{30}_{15}Si \)
• Resulting particle: \(\ 1e^0 \) (a beta particle or electron)

 

2. Applying conservation of charge and mass number:

• Original mass number: 30 (for silicon)
• Original atomic number: 15 (for silicon)
• Mass number is conserved: Therefore, the sum of mass numbers on the left stays 30.
• The net charge must remain the same before and after the reaction, meaning the input atomic number must be adjusted for the addition of the beta particle.

 

3. Identify the missing components: If a beta decay process is occurring, a neutron is converted to a proton, releasing the beta particle. Therefore, expect the atomic number on the reaction product side to increase by 1 to 16 (phosphorus, P) while the mass number remains at 30.

Thus the balanced equation is: \(\ ^{30}_{15}Si \rightarrow \ ^{30}_{16}P + 1e^0 \)

4. Therefore, the completed equation is consistent with option \(( 0 + 1e^0 )\) as a notation adjustment, aligning with our balanced equation where the resulting component supports charge and mass conservation.

In conclusion, the completion involves recognition of the process results and maintaining the balance using the chosen option.

Answer 2

This question asks us to complete the beta decay equation for silicon-30, where a nucleus emits an electron (represented as \( 1e^{0} \)) and transforms into another element. We check what needs to go in each blank by testing the four options against the rules of nuclear equation balancing, where the top numbers (mass numbers) must add up equally on both sides and the bottom numbers (atomic numbers) must add up equally on both sides.

1. + 1e^0: This option leaves the first blank empty, but a nuclear equation needs a definite entry there, since beta decay is a spontaneous process where no particle is absorbed by the silicon nucleus. Leaving it blank does not properly represent that nothing is captured, so this option is incomplete.
2. 0 + 1e^0: Silicon-30 has mass number 30 and atomic number 15. In beta decay, a neutron inside the nucleus turns into a proton, and an electron is thrown out. Since no particle is absorbed from outside, the first blank is correctly filled with 0. On the product side, the mass number stays at 30 and the atomic number rises to 16, which is phosphorus-30, and the electron carries mass number 0 and charge -1, written as \( 1e^{0} \). Checking the balance: the mass numbers give \( 30 + 0 = 30 + 0 \), and the atomic numbers give \( 15 + 0 = 16 - 1 \), both of which hold true. This option correctly completes the equation.
3. 0 - 1e^0: This option repeats the electron term on the input side instead of showing it as a decay product, which does not reflect what actually happens in beta decay, since the electron is created and ejected, not absorbed. Placing it before the reaction with a minus sign does not correctly balance the equation.
4. None: Since option 2 balances both mass number and atomic number correctly, an answer does exist among the choices, so "None" cannot be right.

Working through the conservation of mass number and atomic number confirms that silicon-30 decays by emitting a beta particle to form phosphorus-30, with nothing entering the reaction from outside. This matches the completion \( 0 + 1e^{0} \).

Therefore, the correct answer is 0 + 1e^0.